CN117685123A - High-pressure common rail fuel system fuel injection rule prediction method based on rail pressure fluctuation model - Google Patents
High-pressure common rail fuel system fuel injection rule prediction method based on rail pressure fluctuation model Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F02D41/00—Electrical control of supply of combustible mixture or its constituents
- F02D41/30—Controlling fuel injection
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Abstract
The invention discloses a rail pressure fluctuation model-based high-pressure common rail fuel system fuel injection rule prediction method, which belongs to the technical field of diesel engine fuel systems and comprises the following steps: 1) Establishing a rail pressure fluctuation model; 2) Establishing a discretized state space model according to the rail pressure fluctuation model in the step 1); 3) Rail pressure fluctuation optimal estimation based on Kalman filter; 4) And calculating an oil injection rule by using the optimal rail pressure drop estimation result. The rail pressure observer based on Kalman filtering is designed on the basis, and the rail pressure dropping process obtained by observation is utilized to realize real-time observation and calculation of the oil injection rate and the oil injection quantity of the high-pressure common rail system.
Description
Technical Field
The invention belongs to the technical field of diesel engine fuel systems, and particularly relates to a fuel injection rule real-time prediction method suitable for a high-pressure common rail fuel system.
Background
At present, the fuel injection quantity control of a high-pressure common rail system of a diesel engine is an open-loop control mode based on a calibration MAP, and fuel injection information cannot be measured in real time in the actual operation process, and due to the influence of factors such as system operation condition change and structural parameter degradation, consistency and reliability of circulating fuel injection performance are often difficult to ensure. If the injection information can be monitored in real time in the actual running process of the diesel engine, the injection rule is subjected to closed-loop adjustment and correction, and the accuracy of injection control can be greatly improved.
The instantaneous pressure drop caused by the fuel injection process directly reflects the fuel injection process information, and the current fuel injection prediction research based on the fuel pressure signal mainly comprises the steps of establishing a dynamic mathematical model, carrying out numerical solution calculation on the dynamic mathematical model to obtain the fuel injection quantity, wherein the methods are essentially open-loop calculation, and the calculated fuel injection quantity result has larger errors due to factors such as modeling errors, improper initial condition setting, noise interference and the like. Aiming at the limitation, the inventor has applied for 'a high-pressure common rail system fuel injection quantity prediction method based on a closed-loop observer', introduces a closed-loop feedback correction idea, and realizes the real-time observation and closed-loop correction of the circulating fuel injection quantity (China patent: ZL202010577723.3, which is authorized). On the basis, when the rail pressure changes in a large range, the model parameters change along with the working condition, the system has larger nonlinearity, the inventor optimizes the observation process by adopting a Kalman filtering algorithm, and can perform continuous loop iteration and rolling optimization on the estimated value and the feedback gain of the state variable (Chinese patent: CN 2022112886412). However, the above method only considers the influence of the oil injection process on the pressure fluctuation, namely, only models the situation that the oil injection process is not supplied with oil, and is suitable for the situation that the oil injection process is not overlapped with the oil supply process. When the oil supply process and the oil injection process are overlapped, the rail pressure reduction process caused by oil injection is affected by the oil supply process, and the established oil injection observation model is not applicable any more.
Disclosure of Invention
In order to solve the problems, the invention provides a rail pressure observer based on Kalman filtering, which is designed on the basis of the rail pressure observer based on Kalman filtering, and realizes real-time observation calculation of the oil injection rate and the oil injection quantity of a high-pressure common rail system by taking the rail pressure drop process caused by oil injection and the rail pressure rise process caused by oil supply into consideration. And (3) injection: in the invention, (. Cndot.) is the first derivative, (. Cndot.) is the second derivative and (. Cndot.) is the estimated value.
The technical scheme adopted by the invention is as follows:
a method for predicting a fuel injection rule of a high-pressure common rail fuel system based on an optimized rail pressure fluctuation model comprises the following steps:
1) Establishing a rail pressure fluctuation model;
2) Establishing a discretized state space model according to the rail pressure fluctuation model in the step 1);
3) Rail pressure fluctuation optimal estimation based on Kalman filter;
4) Calculating an oil injection rule by using an optimal rail pressure drop estimation result;
wherein, step 1) establishes the rail pressure fluctuation model as:
the rail pressure change p being the subtraction of the steady state value p ss The instantaneous rail pressure fluctuation after is formed by superposition of an ascending process and a descending process, and is expressed as follows:
p(t)＝p down (t)+p up (t) (1)
wherein, the rail pressure decline stage model:
scaling factor K down (p ss )＝K(p ss )·α(p ss ) The value of the fuel injection valve is equal to the ratio of the rail pressure drop amount in the fuel injection process to the corresponding fuel injection pulse width; k is a proportionality coefficient, the value of which depends on the target rail pressure; τ down For injecting fuelA time constant of the rate output response;
C loss is the fuel loss coefficient, the value of which is Q inj And Q is equal to loss Ratio of steady state value p ss For the current working condition target rail pressure, V 0 For the initial volume of the common rail, deltaV (p ss ) For the volume compensation of the common rail pipe, the oil injection time sequence signal u inj (t) is a pulse width modulated signal
The period T is the oil injection interval, and the oil injection starting time T start Determined by the beginning descending moment of rail pressure and ending moment t end Determined by the duration of the injection;
track pressure rising stage model:
p up (t) is the rail pressure rise, τ up Inertial time constant of output response for rail pressure rise process, proportionality coefficient K up (p ss ) Is the ratio of the rail pressure rise to the corresponding oil supply;
u pump (t) is the step input of the oil supply quantity, the amplitude of the step input signal is the reference oil supply quantity of the current working condition, and the action time t of the step input step Can be determined by the moment when the rail pressure starts to rise;
the discretized state space model in step 2) is:
where k represents the number of sampling points,C d ＝C＝[1 0 1]the method comprises the steps of carrying out a first treatment on the surface of the The output y is the instantaneous rail pressure fluctuation p after subtracting the steady state value; input signal u= [ u ] inj u pump ] T ；Comprising the rail pressure drop p down Rail pressure drop Rate->Track pressure rise p up Three variables are used as state variables;
the step 3) of rail pressure fluctuation optimal estimation based on a Kalman filter comprises the following steps:
consider model uncertainty w u (k) And measuring noise v (k), the discrete system state space model being expressed as:
wherein the process noise w is input u (k) Is [ w ] inj (k)w pump (k)] T ；w u (k) Zero-mean Gaussian white noise which is assumed to be uncorrelated with v (k) has covariance matrices of Q and R respectively;
due to B in the model (19) d The process noise covariance matrix Q can be optimally designed into a time-varying matrix to adapt to the working condition change along with the change of the rail pressure working condition:
Q(k)＝B d (k)E[w u (k)w u (k) T ]B d (k) T (6)
at a set initial valueAnd P (0) + After Q and R are set, the method comprises the steps of,
(1) calculating a priori estimates
(2) Calculating covariance matrix P (k) of prior estimation error - ：
P(k) - ＝Α d (k-1)P(k-1) + Α d (k-1) T +Q(k-1) (8)
(3) According to P (k) - Calculating a Kalman feedback gain K (K):
K(k)＝P(k) - C d (k) T [C d (k)P(k) - C d (k) T +R(k)] -1 (9)
(4) at the kth time, output by measurement y (k) and a priori estimateThe difference is used as feedback to correct the prior estimated value to obtain the posterior estimated value +.>
(5) Calculating a posterior covariance matrix P (k) + ：
P(k) + ＝(I-K(k)C d (k))P(k) - (I-K(k)C d (k)) T +K(k)R(k)K(k) T (11)
Continuously updating the system state, the error covariance matrix and the Kalman filtering gain through the circulation of the steps (1) to (5), enabling the posterior estimation value to approach to a true value, namely enabling the posterior error to approach to 0, and completing the optimal estimation of the state variable of the high-voltage common rail system;
the step 4) of calculating the fuel injection rule by utilizing the optimal rail pressure drop estimation result comprises the following steps:
using the state variable estimated value of the high-pressure common rail system in the step 3)Calculating the fuel injection rate according to formula (4):
wherein C is loss Is the fuel loss coefficient; at a certain rail pressure p 1 Under the condition, the coefficient and the fuel leakage quantity V leak Oil return amount V re And fuel injection quantity V inj The following are related:
by experimental or simulation means, the set rail pressure p is measured 1 V below leak 、V re And V inj According to formula (14) to obtain C loss (p 1 ) And changing the rail pressure to obtain C under different set rail pressures loss C when the rail pressure is large in range by least square fitting loss (p ss )；
Will beSumming in the oil injection stage to obtain oil injection quantity observation value +.>
The invention has the advantages that:
1. rail pressure change according to oil injection process and oil supply processThe influence of the oil injection and rail pressure drop section and the oil supply and rail pressure rise section is established, and the rail pressure drop quantity p is selected down Rate of rail pressure dropTrack pressure rise p up And constructing an considerable state space model by three variables, wherein the model can be suitable for rail pressure fluctuation observation under the condition that oil supply and oil injection are overlapped.
2. The uncertainty of the model and the influence of measurement noise are considered in the model, and an optimal estimation method of the oil injection rule based on a Kalman filtering algorithm is provided. And updating the feedback gain matrix in real time by using a Kalman filtering recursion principle, and optimally designing a process noise covariance matrix Q for adapting to the change of a large-range rail pressure working condition. Therefore, an optimal estimation result of the rail pressure drop process caused by oil injection is obtained, and the on-line real-time accurate observation of oil injection information is realized.
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In order to more clearly illustrate the technical solutions of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and all other embodiments obtained without the inventive effort to a person skilled in the art are within the scope of protection of the present invention.
FIG. 1 is a schematic diagram of an oil injection law observation method based on rail pressure fluctuation
FIG. 2 is a schematic diagram of a rail pressure fluctuation Kalman filter process
FIG. 3 injection timing input signal
FIG. 4 oil supply step input Signal
FIG. 5 measured rail pressure and observed pressure for non-overlapping fuel injection and delivery
FIG. 6 actual and observed injection rates for non-overlapping fuel injection and delivery
FIG. 7 actual and observed fuel injection amounts when fuel injection and oil supply are not overlapped
FIG. 8 measured rail pressure and observed pressure for overlap of fuel injection and supply
FIG. 9 actual and observed injection rates during overlap of injected fuel and oil
FIG. 10 actual and observed fuel injection quantity when fuel injection and oil supply overlap
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other implementations, which can be made by those skilled in the art without making any inventive effort, are intended to be within the scope of the present invention, based on the examples herein.
Fig. 1 is a schematic diagram of an observation method for a fuel injection rule of a high-pressure common rail system based on optimal rail pressure fluctuation estimation according to an embodiment of the invention. Measuring rail pressure signals in real time through a pressure sensor on the common rail pipe; inputting the signal into a designed rail pressure Kalman filter to obtain an optimal estimation result of a rail pressure drop stage caused by oil injection; calculating the fuel injection rate by using the rail pressure drop estimation result; and (3) carrying out integral calculation on the oil injection rate in the oil injection stage to obtain the predicted oil injection quantity.
FIG. 2 is a schematic diagram of a rail pressure fluctuation Kalman filter design process. Firstly, respectively establishing dynamic models between an oil injection section, a rail pressure descending section and an oil supply section and a rail pressure ascending section according to the influence of an oil injection process and an oil supply process on rail pressure fluctuation; selecting a state variable to construct a rail pressure fluctuation state space model, and discretizing; based on the method, the influence of model uncertainty and measurement noise is considered, a rail pressure fluctuation Kalman filter is designed, the difference between a rail pressure signal measured by a rail pressure sensor in real time and an estimated value is used as feedback to correct, the system state and covariance matrix are continuously updated, and the optimal estimation of the rail pressure drop process is realized.
The following will describe in detail.
Step 1: establishing a rail pressure fluctuation model
Assuming that the fuel pressure of the common rail pipe is uniformly distributed, the common rail pipe fuel continuous equation is expressed as:
wherein p is the subtraction of steady state value p ss Post instantaneous rail pressure fluctuation, steady state value p ss The target rail pressure is the current working condition; q (Q) pump Is the oil supply rate; q (Q) inj The fuel injection rate is; q (Q) loss Is the fuel loss rate; e is the fuel volume elastic modulus; v is the common rail control volume.
Ignoring the fuel temperature change in the working process, wherein E is related to the rail pressure working condition, and the empirical formula is as follows:
E＝1.2×10 4 (1+0.001p ss ) (2)
the common rail pipe is acted by high-pressure fuel, V changes along with the rail pressure working condition, and V is set to be equal to the initial volume V of the common rail pipe 0 And the compensation quantity DeltaV thereof, namely:
V＝V 0 +△V(p ss ) (3)
when in oil injection, the fuel is sprayed out to cause the pressure in the common rail pipe to drop instantaneously; during oil supply, the high-pressure oil pump supplies high-pressure fuel to the common rail pipe, and rail pressure instantaneously rises. To decouple the influence of the injection and supply processes on rail pressure fluctuations, the rail pressure p can be decomposed into a rail pressure drop process p down With rail pressure rise process p up And respectively establishing a relation between an oil injection process and rail pressure drop and an oil supply process and rail pressure rise.
Step 1.1: establishing a model between the oil injection process and the rail pressure drop section
The fuel injection rate Q can be obtained simply by the method (1) inj With rail pressure drop p down Mathematical model between:
wherein C is loss Is the fuel loss coefficient, the value of which is Q inj And Q is equal to loss Ratio of the two components. According to formulas (2) to (4), α (p) ss ) The value of (2) is related to the target rail pressure working condition and can be approximately regarded as constant under a certain rail pressure working conditionA number.
Obviously, there is an integral relationship between the injection rate and the rail pressure drop. Because the oil injection rate signal cannot be obtained in real time in the actual running process, and the oil injection rate can be determined by the oil injection timing and the oil injection pulse width, the invention adopts the oil injection time sequence signal u inj (t) modeling the rail pressure drop phase for input
Oil injection timing signal u inj And (T) is a pulse width modulation signal, the period T of which is the oil injection interval, and the duty cycle of which is the ratio of the duration of oil injection to the oil injection interval. Start time t of fuel injection start Determined by the beginning descending moment of rail pressure and ending moment t end As determined by the duration of the injection. The signal is shown in FIG. 3, and its expression can be described as
Taking into account the injection timing signal u inj (t) and injection Rate Q inj There is some inertia between (t), and the dynamic model between the two can be expressed as:
wherein K is a proportionality coefficient, the value of which depends on the target rail pressure; τ down The time constant of the response is output for the injection rate. As the oil injection rate response starts and ends extremely fast, the inertia time constants under different working conditions are similar, τ down Can be regarded as a constant.
Substituting formula (5) into formula (6) to obtain u inj (t) is input, p down (t) is an output rail pressure drop stage model:
in the formula, the proportionality coefficient K down (p ss )＝K(p ss )·α(p ss ) The value of the pressure drop is equal to the rail pressure drop and phase of the oil injection processThe ratio of the pulse width of the fuel injection should be calculated.
Step 1.2: establishing a model between the oil supply process and the rail pressure rising section
The oil supply rate Q can be obtained by the method (1) pump With rise of rail pressure p up Mathematical model between:
however, the oil supply rate cannot be measured in real time, and the timing signal cannot be constructed due to the undefined duration of the oil supply phase. The reference oil supply V of the current working condition can be obtained only by searching the MAP of the oil supply MAP under the pre-calibrated working conditions (different rotating speeds, rail pressures and fuel metering valve openings) pump The fuel supply amount and the fuel supply rate are in integral relation. The present invention thus constructs an oil supply step signal u pump (t) as input to the rail pressure rise phase. The amplitude of the step input signal is the reference oil supply quantity of the current working condition, and the step input action moment t step Can be determined from the rail pressure rise time as shown in fig. 4.
The rail pressure rising amount p is taken into consideration that certain inertia exists in the pressure rising process up With step input u of oil supply pump The dynamic model between (t) is expressed as:
in the formula, the proportionality coefficient K up Is the ratio of the rail pressure rise to the corresponding oil supply; τ up The inertia time constant of the response is output for the rail pressure rising process, and the value of the inertia time constant can be regarded as a constant under different working conditions.
Although the models of the injection and fueling processes are separately built, these models are equally applicable when they occur simultaneously. The rail pressure change p is a superposition of the rising and falling processes expressed as:
p(t)＝p down (t)+p up (t) (10)
step 1.3: identifying model coefficients
The rail pressure drop stage model comprises two undetermined coefficients: k (K) down And τ down . Wherein K is down The ratio of the rail pressure drop corresponding to one oil injection under the current working condition to the corresponding oil injection pulse width is related to the rail pressure working condition. The invention aims at a high-pressure common rail system of a four-fuel injector and a double-plunger double-acting cam driven high-pressure oil pump, takes rail pressure of 1200bar and working conditions of camshaft rotating speed of 1000r/min as examples, obtains rail pressure drop amounts with different pulse widths, and calculates K down As shown in table 1.
TABLE 1 Rail pressure drop parameters and K down
K under different oil injection pulse widths down Similar, therefore K under the current rail pressure condition down Average-44768. When the rail pressure change is set, the step is repeated to obtain model coefficients under the large-range rail pressure change so as to adapt to calculation under different working conditions. The system fits K under different working conditions down The expression is:
K down (p ss )＝-7769-29.51·p ss (11)
according to the first order system characteristic, the time constant τ down For the time at which the injection rate reaches a 0.632 times steady state value from 0. The rising and falling stages of the fuel injection rate curve under different working conditions are extremely fast, and tau is calculated down Constant value 0.00015.
The rail pressure rising stage model also comprises two undetermined coefficients: k (K) up And τ up . According to formula (8), K up The expression of (c) can be written as:
wherein, according to the structural parameters of the common rail pipe, V 0 ＝29061mm 3 Compensation quantity DeltaV (p ss )＝5.048·p ss 。
In the case of step input, the time constant τ up Taking τ under different conditions for the time of the rail pressure rising output response from 0 to 0.632 times the steady-state amplitude up I.e. 0.0019.
Step 2: constructing a rail pressure state space model and discretizing
And establishing a state space model of rail pressure fluctuation according to the established transfer function model. Selecting the track reduction p down Rate of rail pressure drop p down Rise of rail pressure p up Three variables as state variables, i.e.
From the formulas (7), (9) and (10), the state space model is obtained as follows:
in the method, in the process of the invention,C＝[1 0 1]. The output y is the instantaneous rail pressure change p after subtracting the steady state value; input signal u= [ u ] inj u pump ] T 。
The observability of the system is judged. The observable matrix Lo of the model (13) is calculated as follows:
lo is full of rank, which indicates that the system is considerable and can perform rail pressure drop Kalman filter design.
Before designing Kalman filter observer, it is necessary toThe state space model of the continuous system is discretized. When the sampling step is delta t, the state variable x (t) is t k The derivative of time of day can be approximated as:
the above can be converted into:
in the method, in the process of the invention,
sampling time t in equation (16) k The unified sampling point number k is represented by:
x(k)＝A d x(k-1)+B d u(k-1) (17)
the discrete state space model can be expressed as:
wherein C is d ＝C＝[101]。
Step 3: kalman filter-based optimal estimation of rail pressure drop
Consider model uncertainty w u (k) And measuring noise v (k), the system state space model is expressed as:
wherein the process noise w is input u (k) Is [ w ] inj (k)w pump (k)] T 。w u (k) The covariance matrices of zero-mean Gaussian white noise, which is assumed to be uncorrelated with v (k), are Q and R, respectively.
According to the Kalman filtering algorithm, the kth is definedThe state variable estimation value of the moment isAnd is divided into a priori estimated value->Posterior estimate +.>The algorithm comprises two stages of time updating and measurement updating: and in the time updating stage, a state priori estimated value is calculated by using a system model, and in the measurement updating stage, feedback correction is performed by using an error between the rail pressure measured value and the priori estimated value, and a posterior estimated value is calculated.
The kalman filter performance is determined by the noise covariance matrices Q and R. The measurement noise covariance matrix R is then dependent on the degree of filtering of the measurement signal. Due to B in the model (19) d The process noise covariance matrix Q can be optimally designed into a time-varying matrix to adapt to the working condition change along with the change of the rail pressure working condition:
Q(k)＝B d (k)E[w u (k)w u (k) T ]B d (k) T (20)
at a set initial valueAnd P (0) + After proper Q and R are selected, circulation can be carried out according to formulas (21) to (25), and the system state, the error covariance matrix and the Kalman filtering gain are continuously updated, so that the posterior estimated value approaches to a true value, namely the posterior error approaches to 0, and the optimal estimation of the state variable of the high-voltage common rail system can be completed.
A time updating stage:
(1) calculating a priori estimates using a model (18)
(2) Calculating covariance matrix P (k) of prior estimation error - ：
P(k) - ＝Α d (k-1)P(k-1) + Α d (k-1) T +Q(k-1) (22)
(3) According to P (k) - Calculating a Kalman feedback gain K (K):
K(k)＝P(k) - C d (k) T [C d (k)P(k) - C d (k) T +R(k)] -1 (23)
(4) at the kth time, output by measurement y (k) and a priori estimateThe difference is used as feedback to correct the prior estimated value to obtain the posterior estimated value +.>
(5) Calculating a posterior covariance matrix P (k) + ：
P(k) + ＝(I-K(k)C d (k))P(k) - (I-K(k)C d (k)) T +K(k)R(k)K(k) T (25)
At time k, a posterior estimate is obtained according to equation (24)Is->And->Namely, the optimal estimation results of the rail pressure drop amount and the rail pressure drop rate are obtained, and +.>Namely the rail pressure filtering result +.>
Step 4: calculating fuel injection rule by using rail pressure drop optimal estimation result
ObtainingThereafter, the injection rate may be calculated according to equation (4):
wherein C is loss Is the fuel loss coefficient. A certain set rail pressure p 1 Under the condition, the coefficient and the fuel leakage quantity V leak Oil return amount V re And fuel injection quantity V inj The following are related:
by experimental or simulation means, the set rail pressure p is measured 1 V below leak 、V re And V inj According to formula (27) to obtain C loss (p 1 ) And changing the rail pressure to obtain C under different set rail pressures loss C when the rail pressure is large in range by least square fitting loss (p ss ). C obtained by fitting in this example loss (p ss ) The method comprises the following steps:
C loss (p ss )＝0.2115+5.85×10 -6 ·p ss (28)
will beSumming in the oil injection stage to obtain oil injection quantity observation value +.>
In order to verify the filtering effect and the observation precision of the observation method under different working conditions, the simulation research is carried out by applying the method provided by the invention under the working conditions that the rail pressure is 1200bar and the oil injection pulse width is 1.2 ms. Fig. 5 to 7 are the observations of the common rail pressure, the injection rate, the injection quantity in the case where the injection oil supplies do not overlap. Fig. 8 to 10 show the rail pressure, the injection rate and the injection quantity observed when the ratio of the number of injections per cycle to the number of oil supplies is 6:4. It can be seen that the rail pressure and the oil injection rate can be quickly tracked under both working conditions. Comparing actual values of the observed results of the injection quantity of the single injection, the obtained errors are shown in the following table 2:
TABLE 2 oil injection quantity observation errors under different working conditions
| Working conditions of | Maximum error | Minimum error | Average error |
| Oil injection and oil supply are not overlapped | 4.62％ | 1.06％ | 2.62％ |
| The oil-injection oil supply is overlapped | 4.86％ | 0.20％ | 2.55％ |
。
Claims (1)
1. A method for predicting an oil injection rule of a high-pressure common rail fuel system based on a rail pressure fluctuation model is characterized by comprising the following steps:
1) Establishing a rail pressure fluctuation model;
2) Establishing a discretized state space model according to the rail pressure fluctuation model in the step 1);
3) Rail pressure fluctuation optimal estimation based on Kalman filter;
4) Calculating an oil injection rule by using an optimal rail pressure drop estimation result;
wherein, step 1) establishes the rail pressure fluctuation model as:
the rail pressure change p being the subtraction of the steady state value p ss The instantaneous rail pressure fluctuation after is formed by superposition of an ascending process and a descending process, and is expressed as follows:
p(t)＝p down (t)+p up (t) (1)
wherein, the rail pressure decline stage model:
scaling factor K down (p ss )＝K(p ss )·α(p ss ) The value of the fuel injection valve is equal to the ratio of the rail pressure drop amount in the fuel injection process to the corresponding fuel injection pulse width; k is a proportionality coefficient, the value of which depends on the target rail pressure; τ down Outputting a response time constant for the fuel injection rate;
C loss for fuel loss coefficientHaving a value of Q inj And Q is equal to loss Ratio of steady state value p ss For the current working condition target rail pressure, V 0 For the initial volume of the common rail, deltaV (p ss ) For the volume compensation of the common rail pipe, the oil injection time sequence signal u inj (t) is a pulse width modulated signal
The period T is the oil injection interval, and the oil injection starting time T start Determined by the beginning descending moment of rail pressure and ending moment t end Determined by the duration of the injection;
track pressure rising stage model:
p up (t) is the rail pressure rise, τ up Inertial time constant of output response for rail pressure rise process, proportionality coefficient K up (p ss ) Is the ratio of the rail pressure rise to the corresponding oil supply;
u pump (t) is the step input of the oil supply quantity, the amplitude of the step input signal is the reference oil supply quantity of the current working condition, and the action time t of the step input step Can be determined by the moment when the rail pressure starts to rise;
the discretized state space model in step 2) is:
where k represents the number of sampling points,C d ＝C＝[1 0 1]the method comprises the steps of carrying out a first treatment on the surface of the The output y is the instantaneous rail pressure fluctuation p after subtracting the steady state value; input signal u= [ u ] inj u pump ] T ；Comprising the rail pressure drop p down Rail pressure drop Rate->Track pressure rise p up Three variables are used as state variables;
the step 3) of rail pressure fluctuation optimal estimation based on a Kalman filter comprises the following steps:
consider model uncertainty w u (k) And measuring noise v (k), the discrete system state space model being expressed as:
wherein the process noise w is input u (k) Is [ w ] inj (k)w pump (k)] T ；w u (k) Zero-mean Gaussian white noise which is assumed to be uncorrelated with v (k) has covariance matrices of Q and R respectively;
due to B in the model (19) d The process noise covariance matrix Q can be optimally designed into a time-varying matrix to adapt to the working condition change along with the change of the rail pressure working condition:
Q(k)＝B d (k)E[w u (k)w u (k) T ]B d (k) T (6)
at a set initial valueAnd P (0) + After Q and R are set, the method comprises the steps of,
(1) calculating a priori estimates
(2) Calculating covariance matrix P (k) of prior estimation error - ：
P(k) - ＝Α d (k-1)P(k-1) + Α d (k-1) T +Q(k-1) (8)
(3) According to P (k) - Calculating a Kalman feedback gain K (K):
K(k)＝P(k) - C d (k) T [C d (k)P(k) - C d (k) T +R(k)] -1 (9)
(4) at the kth time, output by measurement y (k) and a priori estimateThe difference is used as feedback to correct the prior estimated value to obtain the posterior estimated value +.>
(5) Calculating a posterior covariance matrix P (k) + ：
P(k) + ＝(I-K(k)C d (k))P(k) - (I-K(k)C d (k)) T +K(k)R(k)K(k) T (11)
Continuously updating the system state, the error covariance matrix and the Kalman filtering gain through the circulation of the steps (1) to (5), enabling the posterior estimation value to approach to a true value, namely enabling the posterior error to approach to 0, and completing the optimal estimation of the state variable of the high-voltage common rail system;
the step 4) of calculating the fuel injection rule by utilizing the optimal rail pressure drop estimation result comprises the following steps:
using the state variable estimated value of the high-pressure common rail system in the step 3)Calculating the fuel injection rate according to formula (4):
wherein C is loss Is the fuel loss coefficient; at a certain rail pressure p 1 Under the condition, the coefficient and the fuel leakage quantity V leak Oil return amount V re And fuel injection quantity V inj The following are related:
by experimental or simulation means, the set rail pressure p is measured 1 V below leak 、V re And V inj According to formula (14) to obtain C loss (p 1 ) And changing the rail pressure to obtain C under different set rail pressures loss C when the rail pressure is large in range by least square fitting loss (p ss )；
Will beSumming in the oil injection stage to obtain oil injection quantity observation value +.>
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